Question

what are two consecutive integers such that two times the first is 43 more than the second

Answer 1

You can think of two consecutive integers as n and n+1, and hence create an equation:
$2n = (n + 1) + 43 = n + 44$
Rearranging the equation by subtracting n from both sides
$n = 44$
Hence, your two consecutive integers are n and n+1 i.e. 44 and 45
You can check this: 44•2 = 88 = 45+43